ME108 Lab: Fatigue Testing
Arnav Chaturvedi, Phillip Downey, Joey Kroeger, Akhi Mishra, David Perez, Qi Zheng
Date Submitted: 30 November 2016 Date Performed: 16 November 2016 Lab Section: 104
GSI: Semih Bezci
Abstract
In this lab we will test fatigue failure due to cyclic loading. We used an Instron cyclic loading machine to test 4 notched 1045 steel samples. Each sample was loaded under different stress amplitudes and we recorded the cycles until failure. We then analyzed crack propagation in the samples using a microscope. We were able to conclude that our model does not accurately predict the experimental data; however, the model does accurately predict the trend of the experimental data.
Introduction: Fatigue is a type of failure caused by cyclic loading at a stress level that is below the static loading failure stress. Fatigue damage can occur below the monotonic yield strength. The fatigue life of a material goes through three stages: crack initiation, crack growth and fracture. 1(p230) In this lab, we studied fatigue life for four different AISI 1045 Steel specimens. We used a cyclic loading machine to test all the specimens, and recorded number of cycles to failure.
The main approaches to study fatigue failure are stress-based approach, strain-based approach, and fracture mechanics approach. The first two approaches are macroscopic, because NF (the number of cycles to failure) is related to “global” driving force of fatigue (stress amplitude ∆ σ , and strain amplitude ∆ ε ). The third approach is microscopic because N F is related to “local” driving force (stress intensity factor range ∆K). In this lab, we focus the stress based approach. The objective of this report was to map the relationship between stress amplitude and fatigue life as a result of the material properties of 1045 steel.
This experiments only encompasses 4 tests with different loads, and no repetition to eliminate outlier errors. As such more testing would be beneficial to confirm the results. Nonetheless, results of this experiment could help engineers decide on materials to be used in cyclically loaded parts such as in car axles or crankshafts.
Theory : Because nearly all engineered components undergo repetitive use rather than singular activation, it is important to consider the effects of cyclic loading on sample material specimens. Fatigue failure occurs at stresses and strains below the critical values (yield strength, namely) of a material and so simple monotonic analysis often paints an incomplete picture of a material’s reaction. The cyclic loading will result in an accumulation of microdamage that will eventually lead to material failure. 2(p272) There are three critical phases in which cyclic loading will cause failure. The first is crack initiation. Here, the material will initially form microcracks as the damage accumulates (this is the dominant phase for brittle materials)1 (p235) . Next is the growth stage in which the cracks propagate through the material sample (this is the dominant phase in ductile materials). Finally, the fracture itself occurs as the cracks become large enough (this phase is often ignored because, relatively speaking, the number of cycles here is much smaller than in the other phases) 2(p278). The total number of cycles to failure (also known as the fatigue life, N F) is expressed as the sum of the number of cycles in each of these three phases (though it is often approximated to be the sum of the first two phases)3 (p279) . The number of cycles to failure obtained from this testing can be compared (using an appropriate factor of safety) with design criteria to quantify the likelihood that our final product will fail.
Because the failures can be geometry dependant, it is important to consider the notching on the material specimens that were used in this lab. Adding a notch to a specimen will concentrate the failure
which simplifies analysis because the factors introduced by the gripping mechanism can be ignored and it gives the technician control over where the failure will occur. The reduced cross sectional area of the notched section results in a higher stress for a given load as compared with other sections of the specimen4 (p210) . A comparison can be drawn between the notch geometry and the crack geometry that was discussed in lecture. As the radius of the notch is reduced (as it was on our samples), the stress concentration is significantly higher than a more dog-bone shaped (larger radius) sample 2(p70).
Testing was carried out on an Instron cyclic loading machine in which a mass was applied to bend
a cylindrical sample being rotated about its longitudinal axis. This causes microcracks to form and
eventually grow radially starting from the outer diameter of the sample. When the cracks reach a critical
length towards the center of the sample, the sample will fail. The three stages of fatigue failure (crack
initiation, crack propagation, and sample failure) can be identified in close study of the failed samples
(figures 1-4). As the applied load is increased, the cracks will cause failure more quickly.
Experimental Procedure: Our experiment was centered around a high speed rotating fatigue testing
apparatus. We began with four identical specimens of AISI 1045 Steel rods with machined notches in the
center of the specimen to create a stress concentration at a desired area. Each specimen was loaded into
the machine, one by one. In order to do this, a collet was tightened on each end of the specimen. The
collets were then loaded into each half of the rotating fixture on the machine. After connecting the
specimen to the drive axle of the machine, loading harnesses were attached to either side of the specimen.
These harnesses were connected to a weight stack under the machine that served as the applied load in
each test. Weights were only applied when the machine began spinning the specimen so as to reduce the
likelihood of inducing premature cracks. Once the appropriate load was applied, the machine ran the
specimen through multiple loading cycles until failure while recording the number of cycles. After failure,
the number of cycles was documented and the specimen was placed under a microscope for further
observation. After photographs of the sample were taken, we repeated the procedure for the next sample
until all four specimens had been tested with their respective load.
Results: A comparison between the experimental and calculated results for fatigue testing of AISI 1045
Steel specimens across different loads is provided in the following table. Stress Amplitude was calculated
through the relation: Stress Amplitude = σ = 16×Load×Length . Calculated Cycles to failure is calculated max π×Diameter3
through the relation: N = ( 193 )12.5 which comes from reverse engineering the power-law F Stress Amplitude
relationship discovered from curve-fitting experimental data in Komvopoulos’ Mechanical Testing of Engineering Materials2(p72).
Load (lb)
Number of Cycles to Failure
Length (in)
Diameter (in)
Stress Amplitude (ksi)
Calculated Cycles to Failure
Experimental Error in N F
(Experimental N F)
(N F )
(%)
10
71,585
4.0
0.146
65.5
741,007
935.14%
11
48,603
4.0
0.146
72.0
225,120
363.18%
12.5
25,137
4.0
0.146
81.8
45,546
81.19%
14
11,126
4.0
0.146
91.6
11,046
0.72%
The error between calculations and
results grows to over 935% at the lowest
tested load. The difference in results is
illustrated in the following graph. The
calculated results use the power curve: S
= 193N -.08 . F
The actual results follow the power curve: S = 492*N -.179 .
Further calculations were done for
notched and un-notched AISI 1045 steel.
The following curves were calculated
using the supplemental data which
assumes that Ultimate Tensile Stress is
700 MPa. The calculations can be found
in Appendix A. Notched Stress is lower
for the same N F than unnotched, while
the Experimental stress was lower than
both.
Discussion: Over the course of our testing, we saw our test specimens fracture at a different rate than our adjusted model. Despite this, we still saw the same type of power relationship between stress and number of cycles before fracture that the principles of fatigue testing defined, though with different constants than are given 1045 steel from Komvopoulos 2(p72). The fact that the curve follows the same type of model validates our theory that materials fatigue over repeated cycles at stresses below their failure stress. With greater a stress, the number of cycles to failure drops. Despite the merits of our model, we have a fairly large gap between the expected and resultant curves. This may be as a result of human error; when we first load the weights, the force of the drop could begin the initiation and propagation of cracks. It’s also
F
likely that the assumptions which we used to set up our model are faulty; we do not properly factor in the geometry of our test specimens. The given model in the Komvopoulos lab book is based on a different notch size. The notch geometry in turn changes how the stress concentrates at different points. Komvopoulos’ data uses a large radius notch whereas in this experiment, the samples had a much smaller notch. The smaller size leads to a much higher stress concentration which exacerbates fatigue on the specimen. This leads to lower fatigue life for the same stress amplitudes, or a lower stress amplitude for the same fatigue life. Additionally, the supplemental graphs show how adding a notch to a straight bar significantly reduces the stress amplitude required for the same fatigue life.
We gathered further evidence for the theory by looking at images of the fractured specimens through a microscope (Figures 1-4). The cracks begin on the outer surface of the rod because that’s where the rod experiences the greatest strain amplitude. We can clearly see that as the load increases, the area that fails catastrophically increases based on the area of the dark region in the center of the specimen.
While the tests brought forth valuable information about the ability of steel 1045 to withstand repeated stresses, further testing could be completed using different geometries or a wider range of load weights (stresses) to build upon the model that we have. Based on this information we can estimate the expected lifetime of steel parts under repeated stresses, like those in a car engine. The same style of tests can be used on other materials to find their fatigue properties. For this experiment in particular, we evaluated how the factors of stress amplitude and notch amplitude play a significant role, in conjunction with the material type, on the fatigue life.
Conclusion: After fatigue failure testing 4 samples using cyclic loading, we were able to observe the stages of fatigue failure under a microscope. We then analyzed the general trend for the experimental data and compared it with calculated estimation based on previous data. We concluded that our model does not accurately represent the data that we recorded; however, a similar trend between the model and data was observed. We realized this is due to the fact that we did not use the correct geometry in our model.
Appendix A
Figure 1- 10 lbs applied
Figure 2- 11 lbs applied
Figure 3- 12.5 lbs applied
Figure 4- 14 lbs applied
Appendix B
1. Callister WD, Rethwisch DG. Materials Science & Engineering: An Introduction. #8. Hoboken: John Wiley & Sons Inc.; 2007.
2. Komvopolous, K. Mechanical Testing of Engineering Materials. USA: Cognella; 2011.
3. Hosford WF. Mechanical Behavior of Materials. Cambridge: Cambridge University Press; 2005.
4. Dowling NE. Mechanical Behavior of Materials. #4. San Francisco: Pearson Education; 2012.
I, David Perez, confirm that I wrote the Discussion of the lab report.
I, Arnav Chaturvedi, confirm that I wrote Procedure of the lab report.
I, Phillip Downey, confirm that I wrote the Theory of the lab report.
I, Qi Zheng, confirm that I wrote Introduction of the lab report.
I, Joey Kroger, confirm that I wrote Abstract & Conclusion of the lab report.
I, Akhilesh Mishra, confirm that I wrote Results of the lab report.